1. Field of the Invention
The present invention relates to a tool for and method of measuring, and, more particularly, the present invention relates to in situ, non-destructive determination of the full stress components for thin, flat crystalline solids using poliariscopy.
2. Description of the Related Art
The photovoltaic (PV) industry uses single crystal and polycrystalline silicon in the manufacturing of PV modules. Single crystal wafers are usually grown from a liquid melt into ingots by the Czochralski (CZ) method as shown in FIG. 1. The Czochralski method is used for high volume production of single crystal silicon. A crystal is “pulled” out of a vessel containing liquid silicon by dipping a seed crystal into the liquid which is subsequently slowly withdrawn at a surface temperature of the melt just above the melting point. The diameter of the ingot is determined by the pulling rate and the temperature profile.
Multi crystalline silicon is produced by a number of different methods, including the edge-defined film growth (EFG) method and casting. Wafers produced by the EFG method use a die to define the thickness of the produced silicon wafer as shown in FIG. 2. By adjustment of the temperature profile of the graphite die, the silicon sheet crystallizes with large grains. Usually the shape of the ingot produced by the EFG method is large polygons. Recently the technique has been used to produce large cylinders of material as shown in FIG. 3. The large cylindrical material needs to be flattened out for further processing.
Casting is also used to produce multi crystalline silicon. In the photovoltaic industry, about 60% of solar cells are made from cast wafers with a typical efficiency of 13-16.5%. Multi crystalline silicon is usually cast in a fused silica crucible supported by graphite as shown in FIG. 4. Typically, crystallization starts at the bottom of the crucible where the temperature is lowered below the melting temperature (1450° C.) of silicon.
After casting, silicon wafers are produced by sawing. Microelectronic circuits or photovoltaic devices are fabricated on these substrates through various chemical, physical, and thermal processes.
During the growth of EFG silicon, the temperature of the silicon melt is typically in the range of 1450° C., and it drops to room temperature within 0.5 m from the solid-melt interface. Therefore, a high thermal gradient is unavoidable at the solid-melt interface. A similar situation occurs during the crystallization of cast wafers as shown in FIG. 4. Thermal gradients cannot be removed completely, although techniques such as heat exchange method (HEM) systems can reduce the thermal gradient. The magnitude of the thermal stresses is approximately proportional to the curvature of the temperature profile. For this reason, modeling of residual stress usually involves knowledge of the temperature profile, as seen in the work of Bhihe et al. and Lambropoulos et al. The ensuing thermal processing in cell manufacturing, such as oxidation and diffusion, may also introduce non-uniform heating and cooling that results in a substantial thermal gradient and may introduce additional residual stresses. A combination of thermal and mechanical stresses caused during production is frozen into the wafers in the form of strain, which can be reduced but not completely removed by post growth annealing.
Residual stresses may enhance the performance of a mechanical structure and the effects of residual stresses on fatigue are covered in detail elsewhere. Residual stresses can raise or lower the mean stress experienced over a fatigue cycle and an example of how this influences metal structures can be seen in the improvement of the fatigue life. The static loading performance of brittle materials can be improved markedly by the use of residual stresses. Common examples include thermally toughened glass and pre-stressed concrete. For plastically deformable materials, the residual and applied stresses can only be added together directly until the yield strength is reached. In this respect, residual stresses may accelerate or delay the onset of plastic deformation.
In many cases, unexpected failure occurs due to the presence of residual stresses that have combined with the service stresses to shorten component life. Furthermore, in natural or artificial multiphase materials, residual stresses can result in differences in thermal expansion, yield stress, and stiffness. Residual stresses in silicon may cause mechanical failure during processing and change the optical or electrical properties of the wafer. Tensile residual stresses in silicon will lead to crack growth and reduced electron-hole lifetime and wafer breakage. High tensile stresses will also cause unexpected failure during processing of cells when service stresses are introduced. Furthermore, the regions close to the wafer edges may contain micro-cracks which will eventually propagate and fracture the cell in handling during subsequent device fabrication since cracks will propagate in the region of tensile residual stresses.
As strain due to thermal gradient is introduced during growth, the crystal will relieve the residual stresses by the generation and propagation of dislocations. The relationship between residual stresses and dislocation density in silicon wafers was studied by V. Garcia and an inverse correlation was found between residual stresses and dislocation etch pits. It is believed that this will eventually impact the lifetime and thus the efficiency of photovoltaic cells. As the sheet becomes thinner, the grown-in residual stresses, coupled with the stresses imposed during manufacturing, present a formidable challenge. There has been a significant effort to develop non-destructive techniques that expose the in-plane residual stresses, but that prior work is neither fast enough nor sensitive enough to implement in the manufacturing of solar cells.
All stress measurement techniques can be divided into one of two classes: one measures actual strain, and the other measures changes in strain. Residual stress measurement techniques may also be classified by whether the technique is destructive or non-destructive. The choice of a measurement technique should be based on the kind of information needed so it is important to recognize the limitations of each technique. Non-destructive methods are needed for in situ quality monitoring for photovoltaic processing. The most commonly used non-destructive methods are x-ray diffraction, ultrasonic microscopy, shadow Moiré, neutron diffraction, and photoelasticity.
X-ray diffraction detects the strain-induced changes in the crystal lattice, which can then be used to obtain the residual stresses. The sensitivity of this technique is reported to be around 10 MPa. X-ray diffraction measures strains within the surface depending on the x-ray source. Penetration of the specimen by the x-ray beam is related to a number of factors, including material density and beam energy. Generally speaking, the information in the diffracted beam comes from a volume that is about 8 to 20 μm below the surface, and the volume is always slightly larger than the beam size due to scattering.
Ultrasonic microscopy refers to the measurement of residual stresses by the propagation of acoustic waves in a medium under different stresses. Changes in ultrasonic speed can be observed when a material is subjected to stress, the changes providing a measure of the stress averaged along the wave path. The acoustoelastic coefficients necessary for the analysis are usually calculated using calibration tests. A main difficulty of this technique is that the relative change in wave speed is very small, typically of the order of 10−5 MPa−1. The method provides a measure of the macro-stresses over large volumes of material. Ultrasonic wave velocities can depend on micro-structural inhomogeneities, and there are difficulties in separating the effects of multi-axial stresses. Therefore, acoustoelastic microscopy is especially useful in materials uniform both in microstructure and composition, such as single crystal silicon.
Shadow Moiré can detect the residual stresses in circular or rectangular plates. The technique depends on deforming a sample and then comparing the deformation to an analysis and deflection. S. Danyluk and his research group have developed the analytical theory for beam, rectangular and circular plates and used this analysis to extract residual stresses from the displacement measured by shadow Moiré. The limitation of this method is that a certain profile needs to be assumed for the residual stresses. For example, an axis-symmetrical profile is assumed for circular plate. Since the residual stresses are forced to comply with the assumed profile, this technique is not sensitive to the local stress concentrations.
Neutrons have an advantage over x-rays since the wavelengths are comparable to the atomic spacing and their penetration into engineering materials is typically many centimeters. The technique allows for collection of a full stress tensor, or simple tri-axial stresses, depending on how many vectors are measured. Beam penetration is about 152 mm in aluminum, 38 mm in iron and steel, and varies significantly materials such as titanium and zirconium. Unfortunately, since this technique requires a nuclear reactor to supply the neutrons, its use is limited by access to these facilities, and the technique can be prohibitively expensive.
Photoelasticity is an experimental method to determine the stress distribution in a material where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress distribution even around abrupt discontinuities in a material. The method serves as an important tool for determining the critical stress points in a material and is often used for determining the stress concentration factors in irregular geometries.
The method is based on the property of birefringence, which is exhibited by certain transparent materials. Birefringence is a property where a ray of light passing through a material experiences two refractive indices. The property of birefringence or double refraction is exhibited by many optical crystals, but photoelastic materials exhibit the property of birefringence only on the application of stress and the magnitude of the refractive indices at each point in the material is directly related to the state of stress at that point. When a ray of light passes through a photoelastic material, it becomes polarized and gets resolved along the two principal stress directions and each of these components experiences different refractive indices. The difference in the refractive indices leads to a relative phase difference between the two component waves, which is usually called phase retardation as shown in FIG. 5, where H indicates horizontally polarized, V indicates vertically polarized, and δ indicates phase retardation. The magnitude of the relative retardation is given by the stress optic law.
Photoelasticity can be applied to three and two dimensional states of stress. However, the application of photoelasticity to the two dimensional plane stress system is much easier to analyze, especially when the thickness of the sample is much smaller as compared to dimensions in the plane. In this case, stresses act only in the plane of the solid, as the other stress components are zero. The experimental setup to evaluate photoelastic behavior varies from experiment to experiment, but the two basic kinds of setup used are the plane polariscope and circular polariscope.
A commonly used technique to obtain the photoelasticity parameters using a polariscope is phase stepping. The phase stepping concept for photoelasticity was first introduced by F. Hecker and B. Morche, who used plane and circular polariscopes to extract the isochromatic and isoclinic angles, respectively. The stepping technique records multiple images comprising individual picture elements or pixels. The number of images recorded is normally three to ten images or steps, corresponding to different alignments of optical components in the polariscope and uses the image intensities to solve for the photoelastic parameters for each pixel. Calibration methods using applied known stresses (four point bending) and full-field illumination have been used to calibrate the stress optic coefficients, increase system resolution, and produce full field stress.